The Specification of MB OFDM system has been introduced in this chapter.
Although the transmitter architecture is similar to conventional OFDM system, some properties of channel are induced by the ultra wide bandwidth waveforms and some receiver function blocks should be modified. The following details will be discussed in Chapter 3.
Figure 2.1: OFDM signal with cyclic prefix extension.
Figure 2.2: A digital implementation of appending cyclic prefix into the OFDM signal in the transmitter.
Serial
Figure 2.3: Black diagrams of the OFDM transceiver. Variable Length: 0 − 4095 bytes
Pad
12 bits Scrambler Init 2 bits
Figure 2.4: PLCP frame format of the MB OFDM system.
Binary Input
Packet Sync Sequence 21 OFDM symbols
Channel Est Sequence 6 OFDM symbols 9.375 µs
Frame Sync Sequence 3 OFDM symbols 0 ... 0 C0 C1 ... C127 0 0 0 0 0
PS0 PS1 PS20 FS0 FS1 FS2 CE0 CE1 CE5
0 ... 0 −C0 −C1 ... −C127 0 0 0 0 0
Figure 2.5: Standard PLCP preamble format of the MB OFDM system
Packet Sync Sequence 9 OFDM symbols
Channel Est Sequence 6 OFDM symbols
5.625 µs
Frame Sync Sequence 3 OFDM symbols 0 ... 0 C0 C1 ... C127 0 0 0 0 0
PS0 PS1 PS8 FS0 FS1 FS2 CE0 CE1 CE5
0 ... 0 −C0 −C1 ... −C127 0 0 0 0 0
Figure 2.6: Shortened PLCP preamble format of the MB OFDM system
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17
LSB MSB S1S2
LENGTH (12 bits)
SCRAMBLER (2 bits)
R: Reserved
Transmit Order (from left to right) R R1 R2 R3 R4
RATE (5 bits)
R 18 19 20 21 22
R
23 24 25 26 27 R R R
R R5 R R
Figure 2.7: PHY header bit assignment of the MB OFDM system
Figure 2.8: The transmitter architecture of MB OFDM system
Scrambler Convolutional DAC
Encoder Puncturer Bit
Interleaver
Constellation Mapping
IFFT Insert Pilots Add CP & GI
Time-Frequency Code
exp(j2πfct) Input
Data
x
14x
13… x
2x
1x
15Data in
Scrambled data out
Figure 2.9: Scrambler/descrambler schematic diagram in MB OFDM system
D D D D D D
Input Data
Output Data A
Output Data B Output Data C
Figure 2.10: Convolutional encoder: rate R = 1/3, constraint length K = 7
X0
Figure 2.11: An example of the bit-stealing and bit-insertion procedure (R=1/2)
X4
Figure 2.12: An example of the bit-stealing and bit-insertion procedure (R=5/8)
X2
Figure 2.13: An example of the bit-stealing and bit-insertion procedure (R=3/4)
5 15 25 35 45 55
Figure 2.14: Guard subcarrier creation based on edge subcarriers of the MB OFDM symbol
Figure 2.15: Frequency of operation for the MB OFDM system
GROUP 1 GROUP 2 GROUP 3 GROUP 4
Band
GROUP 1 GROUP 2 GROUP 3 GROUP 4
Band
#14
10296 MHz
GROUP 5
Table 2.1: Rate-dependent parameters of PHY header for the MB OFDM system Reserved 01001, 01011–11111
Table 2.2: The data rate dependent modulation parameters of the MB OFDM system
Data
Table 2.3: Scrambler seed selection of PHY header for the MB OFDM system Seed identifier (b1, b0) Seed value (x14 … x0)
0,0 0011 1111 1111 111
0,1 0111 1111 1111 111 1,0 1011 1111 1111 111 1,1 1111 1111 1111 111
Table 2.4: Modulation-dependent normalization factor KMOD for OFDM symbols
Modulation KMOD
QPSK 1/ 2
Table 2.5: QPSK encoding table for OFDM symbols Input bit (b0 b1) I-out Q-out
00 -1 -1
01 -1 1
10 1 -1
11 1 1
Table 2.6: Time frequency interleaving codes and associated preamble patterns for the MB OFDM system
Chapter 3
Intercarrier Interference (ICI) Compensation in IEEE 802.15.3a Multi-band OFDM System
Due to its wide bandwidth, a new UWB channel model is developed by the IEEE 802.15.3a standard and is described in this chapter. For highly dispersive channels, some conventional OFDM receiver algorithms are not suitable anymore. In this chapter, the indoor UWB channel model and conventional synchronization techniques for the IEEE 802.15.3a MB OFDM system will be introduced first. Then, the zero padded prefix (ZPP) OFDM system will be introduced in the following section. In addition, the phenomenon and the equalization scheme for long delay spread channels will be described. Finally, the performance simulations are shown in Section 3.5.
3.1 Indoor UWB Channel Model
All wireless systems must be able to deal with the challenges of operating over a multipath propagation channel, where objects in the environment can cause
multiple reflections to arrive at the receiver. The different multipath components (MPCs) are characterized by different delays and attenuations. The correct modeling of the parameters describing the MPCs is the art of channel modeling [15][16].
For narrow-band systems, these reflections will not be resolvable by the receiver when the narrow-band system bandwidth is less than the coherence bandwidth of the channel. When there are a large number of arriving paths at the receiver within its resolution time, the central limit theorem is commonly invoked in order to model the received envelope as a Rayleigh random variable. However, in UWB systems, the large bandwidth of UWB waveforms significantly increases the ability of the RX to resolve the different reflections in the channel. This large bandwidth can give rise to two effects. First, the number of reflections arriving at the receiver within the period of a very short impulse becomes smaller as the duration of the impulse gets shorter and shorter, so the central limit theorem used to justify a Rayleigh distribution for the receiver signal envelop is no longer applicable. Second, the multipath components may be resolved on a very fine time scale (proportional to the inverse of the signal bandwidth), and the time of arrival of the multipath components may not be continuous. This phenomenon could explain the “clustering”
of multipath components. For a realistic performance assessment, a UWB channel model like the 802.15.3a standard model has to include all those effects.
Three main indoor channel models were considered: the tap-delay line Rayleigh fading model [17], the Saleh-Valenzuela (S-V) model [18], and the ∆-K model described in [19]. These models use a statistical process to model the discrete arrivals of the multipath components. However, the S–V model is unique in its approach of modeling arrivals in clusters, as well as rays within a cluster. This extra degree of freedom yielded better matching of the model to the channel characteristics gathered from measurement data. As a result, the IEEE 802.15.3a standards body selected the
S–V model, which then needed to be properly parameterized in order to accurately reflect the unique characteristics of the measurements.
3.1.1 Saleh-Valenzuela Model
The S-V model models the multipath of an indoor environment for wideband channels. In order to capture this effect, The S-V model distinguishes between
“cluster arrival rates” and “ray arrival rates,” where the first cluster starts by definition at time t = 0, and the rays within the cluster arrive with a rate, given by a Poisson process with a start time relative to the cluster arrival time.
Though, the original S-V model has the characteristic that the amplitude statistics sufficiently match the Rayleigh distribution, the power of which is controlled by the cluster and ray decay factors. However, in UWB channels the amplitudes do not follow a Rayleigh distribution. Rather, either a lognormal or Nakagami distribution can fit the data equally well, which has been verified using Kolmogorov-Smirnov testing with a 1 percent significance level. According to these results, the S-V model was modified for the IEEE model by prescribing a lognormal amplitude distribution. The model also includes a shadowing term to account for total received multipath energy variation that result from blockage of the line-of-sight path. The impulse response of multipath model is described as
( ) ,
(
,)
0 0
L K
i i i
i i k l l k l
l k
h t X α δ t T τ
= =
=
∑∑
− − (3.1)where αk li, are the multipath gain coefficient, T is the delay of the lth cluster, li τk li, is the delay of the kth multipath component relative to the lth cluster arrival time T , li
X represents the lognormal shadowing, and i refers to the ith realization. i
By definition, we have τ = . The distribution of cluster arrival time and the 0,l 0 ray arrival time are given by the independent interarrival exponential probability
density function of a path within each cluster. The channel coefficients are defined as follows:
, , ,
k l pk l l k l
α = ξ β (3.4)
where ξ reflects the fading associated with the lth cluster and l β corresponds to k l, the fading associated with the kth ray of the lth cluster, the small-scale amplitude statistics were modeled as a lognormal distribution rather than the Rayleigh distribution, whichwas used in the original S–V model, which is reflected in the following equations
(
,) (
, 12 22)
, ( , 1 2)2020 log10 ξ βl k l ∝Normal µ σk l, +σ or ξ βl k l =10µk l+ +n n (3.5) where n1 ∝Normal 0,
(
σ12)
and n2 ∝Normal 0,(
σ22)
are independent and correspond to the fading on each cluster and ray, respectively. σ is standard 1 deviation of cluster lognormal fading term (dB). σ is standard deviation of ray 2 lognormal fading term (dB).The behavior of the averaged power delay profile is
, the first cluster, and pk,l is equiprobable ±1 to account for signal inversion due to reflections. The µk,l is given by
Then, the large-scale fading coefficient is also modeled as a log-normal random
variable in order to capture shadowing effects in the channel. the lognormal shadowing of the total multipath energy is captured by the term, X , the total energy i contained in the terms αk li, is normalized to unity for each realization. This shadowing term is characterized by the following
20 log10( )Xi ∝Normal(0,σx2) (3.8)
Note that, a complex tap model was not adopted here. The complex baseband model is a natural fit for narrowband systems to capture channel behavior independently of carrier frequency, but this motivation does not work for UWB systems where a real-valued simulation at RF may be more natural. Figure 3.1 illustrates the equivalent model for simulation of passband system in terms of complex baseband system. Therefore the real-valued passband multipath channel response is simplified as follow
( )
( )
where α is the real-values channel coefficient. The equivalent baseband multipath i channel response is described by
( ) 2
( )
i( )
The UWB model parameters were designed to fit measurement results, and Table 3.1 provides the results of this fit for four kinds different channel scenarios (LOS refers to line of sight, NLOS to non-LOS).
(1). CM1 is based on LOS (0 – 4 m) channel measurements.
(2). CM2 is based on NLOS (0 – 4 m) channel measurements.
(3). CM3 is based on NLOS (4 – 10 m) channel measurements.
(4). CM4 is generated to fit a 25 ns RMS delay spread to represent an extreme
NLOS multipath channel.
As shown in Figures 3.2 and 3.3, along with the channel measurement characteristics listed in Table 3.1, highlight characteristics of the multipath channel that are important to discuss. The multipath spanning several nanoseconds in time result in ISI when UWB pulses is closely spaced in time. However, there are many way to mitigate the interference through proper waveform design as well as signal processing and equalization algorithms. Besides, the extremely wide bandwidth of a transmitted pulse results in the ability to individually resolve several multipath components.
3.2 Receiver Architecture
One of the major drawbacks of OFDM systems is its high sensitivity to synchronization errors. Without accurate synchronization algorithm, it is not possible to reliably receive the transmitted data. In a MB OFDM system, the preamble is used for the sake of synchronizing OFDM signals. In the following section we will introduce the receiver architecture of the MB OFDM system, as shown in Figures 3.4, in detail [20].
3.2.1 Synchronization
Synchronization is a fundamental assignment for any communication system and should be done before the other work like channel estimation and data demodulation. Synchronization has two parts: timing synchronization and frequency synchronization
Packet Detection
Packet detection is the task of finding an approximate estimate of the start of the preamble of an incoming data packet as best it can. Because it is the first synchronization algorithm, the rest of the synchronization process is dependent on good packet detection performed. Fortunately, the preamble of the MB OFDM system has been designed to help the detection of the start edge of the packet. The cross-correlation method takes advantage of the periodicity of the synchronization symbols at the start of the preamble. As shown in Figure 3.5, the matched filter with the coefficient of the preamble sequence is proposed to correlate the received symbols. The preamble sequence is pre-assigned by the piconet channel of MAC layer. When some threshold of correlation is exceeded by the output power of the post-matched filter, the receiver will declare a packet detection. The commonly used value of the threshold is more than 250.
Symbol Timing Estimation
When the start of the preamble of an incoming data packet has been captured, the following job is symbol timing estimation finding the precise moment of when individual OFDM symbols start and end. The result of symbol timing estimation will circumscribe the DFT window, and the DFT result is then used to demodulate the subcarriers of the symbol. MB OFDM receiver has knowledge of the preamble available to them, which enables the receiver to use simple cross-correlation based symbol timing algorithm. According to an estimate of the start edge of the packet provided by packet detector, the symbol timing estimation algorithm improves the estimate to sample level precision, as shown in Figure 3.6. The refinement is performed by calculating the cross-correlation of the received signal r and a n known reference s . The known reference k s can be the end of the k
synchronization symbols or the start of the channel estimation symbols. Equation 3.11 shows how to calculate the cross-correlation. The value of n that corresponds to maximum absolute value of the cross-correlation is the symbol timing estimate.
1 2
where the length L of the cross-correlation determines the performance of the algorithm. Larger value improves performance, but also increases the amount of computation required.
Frequency Synchronization
OFDM is highly sensitive to carrier frequency offset. It results in two main phenomena: reduction of amplitude of the desired subcarrier and ICI caused by nearby subcarriers. The first phenomena results from that the desired subcarrier is not sampled at the peak of the sinc function. The reason of second phenomena is that adjacent subcarriers are not sampled at the zero-crossings of their sinc function. The degradation in dB can be approximated by
( )
2where f∆is the frequency error as a fraction of the subcarrier spacing and T is the sampling period.
Frequency Offset Tracking
The data-aided algorithm is appropriate for the MB OFDM system. The preamble allows the receiver to use efficient maximum likelihood algorithm to estimate and correct for the frequency offset, before the actual information portion of the packet starts.
We introduce the algorithm that operates on the received time domain signal as
shown in Figure 3.7. First, the transmitted passband signal is
2 tx
j f nT n n s
y =s e π (3.13)
where s is the baseband signal andn
ftxis the transmitter carrier frequency. The received signal rn is
f is the receiver carrier frequency and rx
tx rx
f∆ = f −f is the difference between the transmitter and receiver carrier frequencies. Let D be the delay between the identical samples of the two repeated symbols. Then, the frequency offset estimator is developed as follows, starting with an intermediate variable z
( )
We observe that an angle of z is proportional to the frequency offset, and the frequency offset estimator is obtained by
ˆ 1
2 s
f z
πDT
∆ = − ( (3.16)
where the (zoperator takes the angle of its argument
Carrier Phase Tracking
There is always some residual frequency error, because the frequency estimation is not accurate. The residual frequency offset results in constellation rotation. This is the reason why the receiver has to track the carrier phase after data symbols are received.
Data-aided tracking of the carrier phase is simple method for MB OFDM system. There are twelve predefined subcarriers among the transmitted data. These special subcarriers are referred to as pilot subcarriers. The receiver can exactly track the carrier phase with these pilots, symbol by symbol. After the DFT of the nth received symbol, the pilot subcarriers R are equal to the product of channel n k, frequency response H and the known pilot symbols k Pn k, , rotated by the residual
Assuming as estimate Hk of the channel frequency response is available, the phase estimate is
If the channel estimate is perfectly accurate, we get the estimator
2 2 2 2 2
There is no the phase ambiguity problem, because the pilot data are known at receiver. However, the channel estimation is not perfectly accurate, thus they contribute to the noise in the estimate.
3.2.2 Channel Estimation
In wideband communication systems, under the assumption of a slow fading channel, in which the channel transfer function is stationary within a packet duration, preambles or training sequences can be used to estimate the channel response for the following OFDM data symbols in the same packet. The channel estimation symbols in the preamble facilitate an powerful estimate of the channel frequency response for all the subcarriers. The quality of the channel estimation can be improved by averaging the two channel estimation symbols, because they are entirely identical symbols. the two received channel estimation symbols R1,k andR2,k are a product of the channel estimation symbol Xk and the channel Hk plus additive white Gaussian noise Nl,k
, , 1,2
l k k k l k
R =H X +N l = (3.20)
Thus the channel estimate can be calculated as
( )
where the channel estimation data power have been selected to be equal to one. The noise samples N1,k and N2,k are statistically independent, thus the variance of their sum divide by two is a half of the variance of the individual noise samples.
3.3 Zero Padded Prefix (ZPP) OFDM System
Due to the IFFT precoding and the insertion of CP at the transmitter, OFDM entails redundant block transmissions and employs simple equalization of
frequency-selective finite impulse response (FIR) channels. At the receiver, intersymbol interference (ISI) and intercarrier interference (ICI) can be eliminated by discarding the CP. Unless zero, flat fades can be removed by dividing each subchannel’s output with the channel transfer function at the corresponding subcarrier. Therefore, most current wireless OFDM-based systems use a CP to eliminate the effect of multipath.
However, the same multipath robustness can be obtained by using a zero padded prefix (ZPP) instead of the CP [21]-[23]. At transmitter, zero symbols are appended after the IFFT-precoded information symbols in each block of the ZPP OFDM transmission. When the number of zero symbols equals the CP length, the ZPP OFDM system can provide the same multipath robustness as the CP OFDM system.
What we have to modify at the receiver is to collect additional samples corresponding to the length of the prefix and to use the overlap-and-add method to obtain the circular convolution structure.
Due to ZPP, the “time domain” received signal of OFDM symbol can be expressed as the length of the ZPP and use an overlap-and-add method, the received signal of
OFDM symbol can be expressed as
From Equation 3.23, we see that the ZPP OFDM system with overlap-and-add method is equivalent to the CP OFDM system, because they have the same overall transceiver transfer function. It is, thus, not surprising that they has identical property:
complexity, spectral efficiency, and multipath robustness.
Though, there are many the same characterizes between two systems. They still have some differences. The most important advantage of using a ZPP is that power backoff at the transmitter can be avoided. When a CP is used, the transmitted signal will have the structure resulting from CP. This correlation in the transmitted signal induces ripples in the average PSD. Because the FCC limits the PSD of UWB, any ripples in the PSD will lead to power back off at the transmitter. In fact, the amount of power backoff to conform to the restriction of FCC is equal to the peak-to-average ratio of the PSD. For a MB OFDM system, this power backoff will arrive at 1.5 dB, which would result in a lower overall range for the system. When the ZPP instead of the CP, the ripples in the PSD can be reduced to zero with enough averaging. The transmitted signal does not have any structure; because it is completely random.
Figures 3.8 and 3.9 indicate the ripples in the PSD for a MB OFDM system that uses a CP and ZPP. From two figures, they show that the ZPP will result in a PSD with zero ripples and a zero power backoff at the transmitter. This implies that the system will achieve the maximum range possible. In addition to the ripples in the PSD, the CP OFDM system has to spend the energy for CP, but the ZPP OFDM system does
not. However, the receiver will pick up larger noise because the ZPP OFDM system
not. However, the receiver will pick up larger noise because the ZPP OFDM system